The Laplace Transform in option pricing

Abstract

The principal aim of the dissertation is to explain the pricing of the most used options under the BSM model using the Laplace Transform and providing MATLAB codes for the implementation of the obtained theoretical results.

The paper is inspired by Fusai’s work (2000) from which it takes the idea to study the application of a mathematical tool such as the Laplace Transform to a financial evaluation problem such as the pricing of the options. In the first two chapters it has been represented the theory needed to understand the whole topic, starting from the definition of stochastic calculus, passing through the presentation of the BSM model, then illustrating the Laplace Transform Calculus and finally explaining the different techniques of numerical inversion.

In the third chapter all the results obtained from the previous parts are combined to achieve the pricing of the European, Lookback, Barrier and Asian options.

In the last section, it has been used MATLAB to provide an experimental support for the conclusions gained since now. Furthermore, we have compared the efficiency of the proposed method with the result obtained using the usual Monte Carlo simulation procedure and the binomial tree.

In the end, it has been presented a comparison between the performances of the different algorithms of numerical inversion.